I am reading "Knowing and Teaching Elementary Mathematics" by Liping Ma. I would highly recommend it for anyone who is dissatisfied with their child's elementary math education. I haven't finished it but the thesis seems to be that when teachers don't have a profound understanding of fundamental mathematics they can't teach it. Shocking, I know.
In the first chapter Dr. Ma points out some of the mathematical errors American teachers inject into simple substitution with regrouping. In a problem like 52-29 they tell kids that "You can't subtract 9 from 2" (which is wrong) or "The 2 has to borrow from his next door neighbor 5" (as if they are two separate numbers and not part of a whole.)
Anyway, to OP's point, it is difficult for a teacher who does not understand or is actually afraid of math to assess a child's math ability. I think that is why many responding parents have seen teachers stubbornly adhere to their curriculum despite poor writing, mistakes or clear indications that a child is ready for more. Many elementary teachers can't go outside the recipe that the curriculum provides because they lack the mathematical training and understanding to do so.
I think this also explains the (to me) baffling popularity of reform curricula like Everyday Math and Investigations. The curriculum packages the teaching of "deep understanding of math concepts" into bite-sized pieces, games and worksheets. The teachers don't really have to understand the math concepts profoundly. They just execute the canned curriculum that somehow teaches concepts deeply all on its own. It's genius marketing by the textbook company.
